Critics of China are fired up over the World Trade Organization's ruling on Friday that Chinese tariffs on American-made SUVs and luxury cars violate international rules, coming as it does amid U.S. allegations of Chinese hacking of U.S. businesses. Echoing the rhetoric that helped President Barack Obama win crucial Ohio votes in 2012, Democrats from the industrial Midwest trumpeted the ruling as a "significant victory" for American manufacturing jobs. “It is time for China to start playing by the rules," said United Steelworkers president Leo Gerard, who urged the White House to "aggressively enforce our trade laws to make sure American workers get a fair shake."

Sorry, but contrary to those who would designate General Motors and Chrysler as champions of some American manufacturing offensive, there is no "car war" raging across the Pacific Ocean.

To begin with, remember that the current trade brouhaha was actually started by the U.S. in 2009, when the Obama administration placed a 35 percent tariff on Chinese tires at the urging of the American steelworkers. That levy was upheld by the WTO in 2011, despite China's reasonable protests, and the duty on U.S. vehicles headed to China began the same year. The WTO has ruled in favor of the U.S. in all the disputes so far, but the actual results have been fairly insignificant: tariffs brought higher prices to U.S. consumers and shifted imports from China to other sources, but didn't materially affect U.S. jobs or stop China from exporting more than 50 million tires to the U.S. last year.

Meanwhile, it's not clear how badly the latest WTO ruling will even hurt China. For one thing, the tariffs didn't actually slow U.S. auto exports to China or hamper the growth of Chinese imports, and China claimed it had stopped enforcing them in December. For another, demand for high-end imported cars are being filled outside of official channels: From BMW SUVs and Ford pickups to Teslas and anything else offering arbitrage opportunities capable of getting around Chinese restrictions, the trade has boosted U.S. auto sales by as much as 35,000 luxury vehicles per year. The WTO's move against the Chinese tariff will simply allow the original manufacturers to take the business back from gray-market entrepreneurs (who were already starting to be rolled up by U.S. prosecutors).

And it's not like our bailed-out car makers were really taking the battle to the enemy. Chrysler has nearly no presence in China, and the new Fiat Chrysler five-year plan calls for keeping U.S. exports basically flat while vastly increasing imports. The debate over Jeep jobs going to China that roiled the 2012 presidential campaign was a red herring, but there is no flood of Jeep exports to China on the horizon that would create U.S. jobs or fix the trade imbalance.

It is GM, however, that truly embodies the falseness of the alleged car war. It is opening four new vehicle assembly plants and a new engine factory in China, and within two years, almost all Cadillac-brand luxury vehicles other than the Escalade SUV will be built there. GM has taken the lead in technology transfers to Chinese partners, incorporating the Baojun and Wuling brands into its portfolio, and has been re-badging partner-developed vehicles with the Chevy "bow tie" logo for export. GM's new family of global Ecotec four-cylinder engines was jointly developed with its Chinese partner SAIC, demonstrating how deeply the U.S. and China flag-bearers are completely intertwined.

Equally important: Below the car-maker level, the U.S. auto-supplier system has already been largely hollowed out by Chinese competition. As the overall U.S. vehicle trade deficit has grown from $100 million in 2004 to $5.3 billion in 2013, the gap in auto-parts gap has also ballooned: from $3.2 billion in 2004 to $10.5 billion last year. The flow of Chinese parts to the U.S. has grown by 700 percent in the last decade. Truth be told, the vehicles we are shipping to China are likely made with so many Chinese-sourced parts, we shouldn't call them exports so much as returns. Again, GM is a key player in this dynamic, with its longstanding pressure on suppliers to match the "China cost" killing some makers and possibly lowering the quality (and safety) of some parts.

In short, the much-ballyhooed conflict with China for automotive supremacy is a phony war, waged rhetorically for domestic political consumption. The WTO finding may have been justified on the facts, but it's not going to change the dynamics of auto imports to the world's most important growing market. That's a game U.S. companies will have to win on their own.

This column does not necessarily reflect the opinion of Bloomberg View's editorial board or Bloomberg LP, its owners and investors.